Question

If `A = <-7 ,1 ,-3 >`, `B = <3 ,6 ,1 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `0.566` rad

Explanation:

`vecC=vecA-vecB=〈-10,-5,-4〉`
The dot product is `vecA.vecC=∥vecA∥*∥vecC∥*cos(vecA,vecC)`

so `cos(vecA,vecC)=(vecA,vecC)/(∥vecA∥*∥vecC∥)`

`∥vecA∥=sqrt(49+1+9)=sqrt59`
`∥vecC∥=sqrt(100+25+16)=sqrt141`
and `(vecA,vecC)=((-7*-10)+(1*-5)+(-3*-4))=70-5+12=77`
`cos(vecA,vecC)=77/(sqrt59*sqrt141)`
`(vecA,vecC)=arccos(77/(sqrt59*sqrt141))`